{
  "id": "2403.07646",
  "version": "v1",
  "published": "2024-03-12T13:29:22.000Z",
  "updated": "2024-03-12T13:29:22.000Z",
  "title": "Diameter of 2-distance graphs",
  "authors": [
    "S. H. Jafari",
    "S. R. Musawi"
  ],
  "comment": "10 pages, 15 figures. arXiv admin note: text overlap with arXiv:2306.15301, arXiv:2403.06132",
  "categories": [
    "math.CO"
  ],
  "abstract": "For a simple graph $G$, the $2$-distance graph, $D_2(G)$, is a graph with the vertex set $V(G)$ and two vertices are adjacent if and only if their distance is $2$ in the graph $G$. In this paper, for graphs $G$ with diameter 2, we show that $diam(D_2(G))$ can be any integer $t\\geqslant2$. For graphs $G$ with $diam(G)\\geqslant3$, we prove that $\\frac{1}{2}diam(G)\\leqslant diam(D_2(G))$ and this inequality is sharp. Also, for $diam(G)=3$, we prove that $diam(D_2(G))\\leqslant5$ and this inequality is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-12T13:29:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple graph",
      "distance graph",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}